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Linear Algebra for MATH 308
Lecture 1: Vectors, Linear Independence, and Spanning Sets
Lecture 2: Operations with Matrices and Vectors
Lecture 3: Systems of Equations
Lecture 4: Determinant
Lecture 5: Eigenvectors and Eigenvalues
Lecture 6: Matrix Inverses and Diagonalization
Lecture 7: Systems of Differential Equations
Lecture 8: Systems of Differential Equations
Quantitative Finance
Several Variables Calculus
Section 1: Functions of Several Variables
Section 2: Limits and Continuity
Section 3: Partial Derivatives
Section 4: Tangent Planes and Linear Approximations
Section 5: The Chain Rule
Section 6: Directional Derivatives and the Gradient Vector
Section 7: Maximum and Minimum Values
Section 8: Lagrange Multipliers
Differential Equations
Section 1: Integrating Factor
Section 2: Separable Equations
Section 3: Compound Interest
Section 4: Variation of Parameters
Section 5: Systems of Ordinary Differential Equations
Section 6: Matrices
Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
Section 8: Homogeneous Linear Systems with Constant Coefficients
Section 9: Complex Eigenvalues
Section 10: Fundamental Matrices
Section 11: Repeated Eigenvalues
Section 12: Nonhomogeneous Linear Systems
Mathematical Probability
Section 1: Probabilistic Models and Probability Laws
Section 2: Conditional Probability, Bayes’ Rule, and Independence
Section 3: Discrete Random Variable, Probability Mass Function, and Cumulative Distribution Function
Section 4: Expectation, Variance, and Continuous Random Variables
Section 5: Discrete Distributions
Section 6: Continuous Distributions
Section 7: Joint Distribution Function, Marginal Probability Mass Function, and Uniform Distribution
Section 8: Independence of Two Random Variables, Covariance, and Correlation
Section 9: Conditional Distribution and Conditional Expectation
Section 10: Moment Generating Function
Section 11: Markov’s Inequality, Chebyshev’s Inequality, and Weak Law of Large Numbers
Section 12: Convergence and the Central Limit Theorem
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Session 11
Session 11
Instructions
The following video covers the material for this session.
After watching the video, you should attempt the homework problems.
When you have finished the material below, you can return to the
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next session
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Watch Video for Session 11
Content
Properties of linear transformations including injective, surjective, and bijective
Matrix representations of linear transformations between vector spaces
The relationship between the matrix for a linear transformation and the range and kernel of the linear transformation
Rank-Nullity Theorem (or Dimension Theorem) for linear transformations
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Homework
7.3 (Nicholson):
3, 4(b,d), 5c, 6(a,c), 11, 12, 14, 18
9.2 (Nicholson):
1b, 1c, 3, 5a, 9d
5.8 (Fioresi):
4,
5.9 (Fioresi):
11
Open Nicholson Homework Assignment
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